If 2x - 3(x + 2) < 5 - 2x < \- x + 2, then ﬁnd the value of x.

Question 71

If 2x - 3(x + 2) < 5 - 2x < - x + 2, then ﬁnd the value of x.

Solution

Expression 1 : $$5 - 2x < -x + 2$$

=> $$2x - x$$ > $$5 - 2$$

=> $$x$$ > $$3$$ ----------(i)

Expression 2 : $$2x - 3(x + 2) < 5 - 2x$$

=> $$-x - 6$$ < $$5 - 2x$$

=> $$2x - x$$ < $$5 + 6$$

=> $$x$$ < $$11$$ ------(ii)

Combining inequalities (i) and (ii), we get : $$3$$ < $$x$$ < $$11$$

Thus, only value that $$x$$ can take among the options = 10

=> Ans - (C)

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